# Compute the amount and the compound interest in each of the following by using the formulae when:

Question:

Compute the amount and the compound interest in each of the following by using the formulae when:

(i) Principal = Rs 3000, Rate = 5%, Time = 2 years

(ii) Principal = Rs 3000, Rate = 18%, Time = 2 years

(iii) Principal = Rs 5000, Rate = 10 paise per rupee per annum, Time = 2 years

(iv) Principal = Rs 2000, Rate = 4 paise per rupee per annum, Time = 3 years

(v) Principal = Rs 12800 , Rate $=7 \frac{1}{2} \%$, Time $=3$ years

(vi) Principal = Rs 10000, Rate 20% per annum compounded half-yearly, Time = 2 years

(vii) Principal = Rs 160000, Rate = 10 paise per rupee per annum compounded half-yearly, Time = 2 years.

Solution:

Applying the rule $\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$ on the given situations, we get:

(i)

$\mathrm{A}=3,000\left(1+\frac{5}{100}\right)^{2}$

$=3,000(1.05)^{2}$

$=\mathrm{Rs} 3,307.50$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 3,307.50-\mathrm{Rs} 3,000$

$=\mathrm{Rs} 307.50$

(ii)

$\mathrm{A}=3,000\left(1+\frac{18}{100}\right)^{2}$

$=3,000(1.18)^{2}$

$=\mathrm{Rs} 4,177.20$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 4,177.20-\mathrm{Rs} 3,000$

$=\mathrm{Rs} 1,177.20$

(iii)

$\mathrm{A}=5,000\left(1+\frac{10}{100}\right)^{2}$

$=5,000(1.10)^{2}$

$=\mathrm{Rs} 6,050$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 6,050-\mathrm{Rs} 5,000$

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 6,050-\mathrm{Rs} 5,000$

$=\mathrm{Rs} 1,050$

(iv)

$\mathrm{A}=2,000\left(1+\frac{4}{100}\right)^{3}$

$=2,000(1.04)^{3}$

$=\mathrm{Rs} 2,249.68$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 2,249.68-\mathrm{Rs} 2,000$

$=\mathrm{Rs} 249.68$

(v)

$\mathrm{A}=12,800\left(1+\frac{7.5}{100}\right)^{3}$

$=12,800(1.075)^{3}$

$=\mathrm{Rs} 15,901.40$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 15,901.40-\mathrm{Rs} 12,800$

$=\mathrm{Rs} 3,101.40$

(vi)

$\mathrm{A}=10,000\left(1+\frac{20}{200}\right)^{4}$

$=10,000(1.1)^{4}$

$=\mathrm{Rs} 14,641$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 14,641-\mathrm{Rs} 10,000$

$=\mathrm{Rs} 4,641$

(vii)

$\mathrm{A}=16,000\left(1+\frac{10}{200}\right)^{4}$

$=16,000(1.05)^{4}$

$=\mathrm{Rs} 19,448.1$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 19,448.1-\mathrm{Rs} 16,000$

$=\mathrm{Rs} 3,448.1$